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In this paper, we present a Computer Vision (CV) based tracking and fusion algorithm, dedicated to a 3D printed gimbal system on drones operating in nature. The whole gimbal system can stabilize the camera orientation robustly in a challenging nature scenario by using skyline and ground plane as references. Our main contributions are the following: a) a light-weight Resnet-18 backbone network model was trained from scratch, and deployed onto the Jetson Nano platform to segment the image into binary parts (ground and sky); b) our geometry assumption from nature cues delivers the potential for robust visual tracking by using the skyline and ground plane as a reference; c) a spherical surface-based adaptive particle sampling, can fuse orientation from multiple sensor sources flexibly. The whole algorithm pipeline is tested on our customized gimbal module including Jetson and other hardware components. The experiments were performed on top of a building in the real landscape.

Human trajectory forecasting is a critical challenge in fields such as robotics and autonomous driving. Due to the inherent uncertainty of human actions and intentions in real-world scenarios, various unexpected occurrences may arise. To uncover latent motion patterns in human behavior, we introduce a novel memory-based method, named Motion Pattern Priors Memory Network. Our method involves constructing a memory bank derived from clustered prior knowledge of motion patterns observed in the training set trajectories. We introduce an addressing mechanism to retrieve the matched pattern and the potential target distributions for each prediction from the memory bank, which enables the identification and retrieval of natural motion patterns exhibited by agents, subsequently using the target priors memory token to guide the diffusion model to generate predictions. Extensive experiments validate the effectiveness of our approach, achieving state-of-the-art trajectory prediction accuracy. The code will be made publicly available.

In this paper, we present a statistical beamforming algorithm as a pre-processing step for robust automatic speech recognition (ASR). By modeling the target speech as a non-stationary Laplacian distribution, a mask-based statistical beamforming algorithm is proposed to exploit both its output and masked input variance for robust estimation of the beamformer. In addition, we also present a method for steering vector estimation (SVE) based on a noise power ratio obtained from the target and noise outputs in independent component analysis (ICA). To update the beamformer in the same ICA framework, we derive ICA with distortionless and null constraints on target speech, which yields beamformed speech at the target output and noises at the other outputs, respectively. The demixing weights for the target output result in a statistical beamformer with the weighted spatial covariance matrix (wSCM) using a weighting function characterized by a source model. To enhance the SVE, the strict null constraints imposed by the Lagrange multiplier methods are relaxed by generalized penalties with weight parameters, while the strict distortionless constraints are maintained. Furthermore, we derive an online algorithm based on an optimization technique of recursive least squares (RLS) for practical applications. Experimental results on various environments using CHiME-4 and LibriCSS datasets demonstrate the effectiveness of the presented algorithm compared to conventional beamforming and blind source extraction (BSE) based on ICA on both batch and online processing.

The present work is devoted to strong approximations of a generalized Ait-Sahalia model arising from mathematical finance. The numerical study of the considered model faces essential difficulties caused by a drift that blows up at the origin, highly nonlinear drift and diffusion coefficients and positivity-preserving requirement. In this paper, a novel explicit Euler-type scheme is proposed, which is easily implementable and able to preserve positivity of the original model unconditionally, i.e., for any time step-size h>0. A mean-square convergence rate of order 0.5 is also obtained for the proposed scheme in both non-critical and general critical cases. Our work is motivated by the need to justify the multi-level Monte Carlo (MLMC) simulations for the underlying model, where the rate of mean-square convergence is required and the preservation of positivity is desirable particularly for large discretization time steps. To the best of our knowledge, this is the first paper to propose an unconditionally positivity preserving explicit scheme with order 1/2 of mean-square convergence for the model. Numerical experiments are finally provided to confirm the theoretical findings.

The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antiderivative of the integrand. It was long believed that this approach suffers from "low-frequency breakdown," meaning that the accuracy of the calculated value of the integral deteriorates when the integrand is only slowly oscillating. Recently presented experimental evidence, however, suggests that if a Chebyshev spectral method is used to discretize the differential equation and the resulting linear system is solved via a truncated singular value decomposition, then no low-frequency breakdown occurs. Here, we provide a proof that this is the case, and our proof applies not only when the integrand is slowly oscillating, but even in the case of stationary points. Our result puts adaptive schemes based on the Levin method on a firm theoretical foundation and accounts for their behavior in the presence of stationary points. We go on to point out that by combining an adaptive Levin scheme with phase function methods for ordinary differential equations, a large class of oscillatory integrals involving special functions, including products of such functions and the compositions of such functions with slowly-varying functions, can be easily evaluated without the need for symbolic computations. Finally, we present the results of numerical experiments which illustrate the consequences of our analysis and demonstrate the properties of the adaptive Levin method.

In this paper, we conduct rigorous error analysis of the Lie-Totter time-splitting Fourier spectral scheme for the nonlinear Schr\"odinger equation with a logarithmic nonlinear term $f(u)=u\ln|u|^2$ (LogSE) and periodic boundary conditions on a $d$-dimensional torus $\mathbb T^d$. Different from existing works based on regularisation of the nonlinear term $ f(u)\approx f^\varepsilon(u)=u\ln (|u| + \varepsilon )^2,$ we directly discretize the LogSE with the understanding $f(0)=0.$ Remarkably, in the time-splitting scheme, the solution flow map of the nonlinear part: $g(u)= u {\rm e}^{-{\rm} i t \ln|u|^{2}}$ has a higher regularity than $f(u)$ (which is not differentiable at $u=0$ but H\"older continuous), where $g(u)$ is Lipschitz continuous and possesses a certain fractional Sobolev regularity with index $0<s<1$. Accordingly, we can derive the $L^2$-error estimate: $O\big((\tau^{s/2} + N^{-s})\ln\! N\big)$ of the proposed scheme for the LogSE with low regularity solution $u\in C((0,T]; H^s( \mathbb{T}^d)\cap L^\infty( \mathbb{T}^d)).$ Moreover, we can show that the estimate holds for $s=1$ with more delicate analysis of the nonlinear term and the associated solution flow maps. Furthermore, we provide ample numerical results to demonstrate such a fractional-order convergence for initial data with low regularity. This work is the first one devoted to the analysis of splitting scheme for the LogSE without regularisation in the low regularity setting, as far as we can tell.

In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.

In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator.

In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in order to test the accuracy in the computation of the coefficients of the three-term recurrence relation, the zeros and weights, as well as the dependence on the parameter $z.$

People living with Type 1 Diabetes (T1D) lose the ability to produce insulin naturally. To compensate, they inject synthetic insulin. One common way to inject insulin is through automated insulin delivery systems, which use sensors to monitor their metabolic state and an insulin pump device to adjust insulin to adapt. In this paper, we present the Metabolic Operating System, a new automated insulin delivery system that we designed from the ground up using security first principles. From an architecture perspective, we apply separation principles to simplify the core system and isolate non-critical functionality from the core closed-loop algorithm. From an algorithmic perspective, we evaluate trends in insulin technology and formulate a simple, but effective, algorithm given the state-of-the-art. From a safety perspective, we build in multiple layers of redundancy to ensure that the person using our system remains safe. Fundamentally, this paper is a paper on real-world experiences building and running an automated insulin delivery system. We report on the design iterations we make based on experiences working with one individual using our system. Our evaluation shows that an automated insulin delivery system built from the ground up using security first principles can still help manage T1D effectively. Our source code is open source and available on GitHub (link omitted).